⚡ Bolt: Vectorize Newton-Raphson iteration loop in MMLE

.jules/bolt.md

@@ -33,3 +33,6 @@
 ## 2025-05-19 - Dot product scalar gradients allocation
 **Learning:** During gradient calculation, `float((e * (-gamma * distance)).sum())` creates two full-size `(N, J)` arrays: one for the scaled distance and one for the element-wise multiplication before reduction.
 **Action:** Replace `(A * B).sum()` with `np.vdot(A, B)` when scalar reduction is needed over matrix multiplication (where `B` can incorporate scalars naturally like `-gamma * np.vdot(A, B)`). This entirely avoids the 2D array allocation overhead and yields order-of-magnitude improvements in scalar gradient components.
+## 2025-05-19 - Vectorizing Newton-Raphson iteration loops
+**Learning:** A Python loop iterating over a large number of items for an iterative process (like the Newton-Raphson steps in M-step optimization) runs very slowly. Furthermore, operations that element-wise multiply and sum across an axis like `(resid * nodes).sum(axis=1)` inside the loop are sub-optimal since they allocate memory and incur looping overhead.
+**Action:** Vectorize simultaneous updates using a boolean masking array `active = np.ones(n_items, dtype=bool)` to filter items actively converging. Replace element-wise multiplication and `.sum(axis=1)` with dense matrix multiplication `resid @ nodes` against broadcast factors. This allows NumPy to leverage C-level loop unrolling and BLAS, resulting in multi-fold runtime speedups for M-steps.

python/fast_mlsirm/estimators/mmle.py

@@ -121,30 +121,54 @@ def fit_mmle_2pl(
 
         a_new = a.copy()
         b_new = b.copy()
-        for i in range(n_items):
-            ai, bi = a[i], b[i]
-            # Newton steps on the item's expected log-likelihood over nodes.
-            for _ in range(25):
-                eta = ai * nodes + bi
-                p = _sigmoid(eta)
-                w = n_iq[i] * p * (1.0 - p)
-                resid = r_iq[i] - n_iq[i] * p
-                g_a = float((resid * nodes).sum()) - ridge_a * ai
-                g_b = float(resid.sum()) - ridge_b * bi
-                h_aa = -float((w * nodes * nodes).sum()) - ridge_a
-                h_bb = -float(w.sum()) - ridge_b
-                h_ab = -float((w * nodes).sum())
-                det = h_aa * h_bb - h_ab * h_ab
-                if abs(det) < 1e-12:
-                    break
-                da = (h_bb * g_a - h_ab * g_b) / det
-                db = (h_aa * g_b - h_ab * g_a) / det
-                ai -= da
-                bi -= db
-                ai = float(np.clip(ai, 1e-3, 10.0))
-                if abs(da) + abs(db) < 1e-8:
-                    break
-            a_new[i], b_new[i] = ai, bi
+
+        # Vectorized Newton steps across all items simultaneously
+        active = np.ones(n_items, dtype=bool)
+        nodes_sq = nodes * nodes
+
+        for _ in range(25):
+            if not active.any():
+                break
+
+            ai = a_new[active]
+            bi = b_new[active]
+
+            eta = ai[:, None] * nodes[None, :] + bi[:, None]
+            p = _sigmoid(eta)
+
+            n_iq_active = n_iq[active]
+            r_iq_active = r_iq[active]
+
+            w = n_iq_active * p * (1.0 - p)
+            resid = r_iq_active - n_iq_active * p
+
+            g_a = resid @ nodes - ridge_a * ai
+            g_b = resid.sum(axis=1) - ridge_b * bi
+
+            h_aa = -(w @ nodes_sq) - ridge_a
+            h_bb = -w.sum(axis=1) - ridge_b
+            h_ab = -(w @ nodes)
+
+            det = h_aa * h_bb - h_ab * h_ab
+            valid_det = np.abs(det) >= 1e-12
+
+            da = np.zeros_like(ai)
+            db = np.zeros_like(bi)
+
+            da[valid_det] = (h_bb[valid_det] * g_a[valid_det] - h_ab[valid_det] * g_b[valid_det]) / det[valid_det]
+            db[valid_det] = (h_aa[valid_det] * g_b[valid_det] - h_ab[valid_det] * g_a[valid_det]) / det[valid_det]
+
+            ai -= da
+            bi -= db
+            ai = np.clip(ai, 1e-3, 10.0)
+
+            a_new[active] = ai
+            b_new[active] = bi
+
+            step_size = np.abs(da) + np.abs(db)
+            still_active = valid_det & (step_size >= 1e-8)
+
+            active[active] = still_active
 
         a, b = a_new, b_new